ST. PETERSBURG, Fla. — It is ironic that Red Sox starter Jake Peavy is the one who purchased the cigar store Indian figure that has become a fixture in the clubhouse and a symbol of their unity and camaraderie. The passionate pitcher is the exact opposite of his stolid, stoic wooden friend.

Peavy is always yelling, exhorting, and emoting on the mound. He doesn’t wear his emotions on his sleeve. They’re draped across his entire uniform, from cap to cleats.

Sometimes, it feels like he either needs an exorcism or an intervention on the mound, but it’s just his way of pushing himself to pitch well, which is exactly what he did Tuesday night in Game 4 of the American League Division Series against Tampa Bay, setting the Sox up for a 3-1 victory and a trip to the AL Championship Series.

There is an old baseball aphorism that momentum is that day’s starting pitcher. Taking the mound a night after the Sox suffered a gut-wrenching 5-4 walkoff loss, Peavy kept his emotions and the Rays in check. He didn’t let the Maddon Men carryover any momentum from Monday night, stymying them for five innings before allowing a run in the sixth.

In the third playoff start of his career, Peavy pitched 5⅔ innings, allowing five hits and one run, while striking out three, with no walks.

“In such an environment you have to stay calm and not let the momentum build,” said Peavy. “The whole time I was out there we didn’t really have a lot of momentum on our side, so I had to do whatever I could do to keep our side as calm as possible, and not give them any kind of momentum other than what they had.

“It was just a fun night, just a hard-fought win.”

The Sox took Peavy off a hook he didn’t deserve by clawing out two runs in the seventh and then adding an insurance run in the ninth to win the game and the series, 3-1.

Now, Peavy, acquired by the Red Sox in a July 30 trade to buttress their rotation, will get to pitch in a championship series for the first time in his career. He helped the Sox get back to the ALCS for the first time since 2008, when they lost to the Rays in seven games.

“It’s what you play for, to have this opportunity with this group of guys I’m as honored and as blessed as I could ever imagine,” said Peavy.

Before the game, Sox manager John Farrell said, “This is the stage in which we acquired Jake to come in and contribute to.”

It was a stage that had been unkind to Peavy previously in his career. In the only two postseason starts, the last of which came in 2006, Peavy was 0-2 with a 12.10 ERA and 19 hits allowed in a combined 9⅔ innings.

His last postseason start, against the Cardinals in the 2006 divisional round, saw him surrender 11 hits and five runs in 5⅓ innings.

What’s a 13-day layoff between starts, when you’ve waited seven years and five days, according to the Sox media notes, to reconstitute your playoff résumé? His hiatus had little effect on Peavy’s effectiveness. He allowed just three hits through five innings.

But Tampa Bay manager Joe Maddon’s mix-and-match approach had four Rays pitchers sporting the same collective zero on the scoreboard as Peavy’s.

Maddon can be quirky, unconventional, and innovative. What he was not Tuesday night was patient. Maddon pulled starter Jeremy Hellickson in the middle of the second after Hellickson loaded the bases on walks to David Ortiz and Mike Napoli and a sharp single to right field by Daniel Nava. The Rays starter had thrown just 22 pitches.

Jamey Wright, the first of eight Rays relievers in the game, came on and got Jarrod Saltalamacchia to strike out looking. Drew then scalded a ball that a leaping James Loney snared at first base and doubled off Napoli.

In the sixth, the Rays broke through against Peavy. Yunel Escobar led off with a double to right that hit the top of the fence and was about a foot from being a home run. Monday night’s hero, Jose Lobaton grounded out to second to move Escobar to third. David DeJesus lined a single to right over the drawn-in infield to break the stalemate.

Peavy retired Wil Myers on a fly ball to left field. He was lifted by Farrell at that point after 74 pitches. Craig Breslow was summoned to face Loney and struck him out.

“Even though he had thrown a limited amount of pitches the game dictated we go to the bullpen,” said Red Sox pitching coach Juan Nieves.

The Sox took the lead in the seventh.

Xander Bogaerts pinch hit for Stephen Drew and drew a one-out walk against Jake McGee, one night after being left on the bench against McGee. Bogaerts scored on a wild pitch by Rays reliever Joel Peralta, who had come on to face Shane Victorino. The Sox took a 2-1 lead when Jacoby Ellsbury, who had singled to move Bogaerts to third, scored from third on an infield single by when Victorino.

The Sox had chances to give Peavy a lead.

They had runners reach second with two outs in both the fourth and the fifth, but couldn’t get the timely hit. Saltalamacchia struck out looking against Game 1 Tampa Bay starter Matt Moore to end the fourth. Alex Torres, who took over in the fifth, got Dustin Pedroia to ground out with runners on first and second to end the fifth.

But all Peavy cared about as he celebrated in a champagne-soaked clubhouse was the win.

There, he expressed the type of raw emotion — joy — that you want everyone to see.